Positioning systems with redundant actuators are widely used in manufacturing and factory automation. In these machines, multiple actuators are available along each axis of motion such that the machine position state is a function (often a sum) of each individual actuator state. In some cases, the states of the entire system can be represented by a linear combination of individual positions of the positioning subsystems.
These machines also have constraints associated with the actuators such as stroke limits, velocity limits, and torque limits. These constraint must be satisfied during operation. Approaches to controlling redundant positioning machines with constraints range from simple ad hoc gain tuning methods to more rigorous mathematical methods, and have been used to compute trajectories that meet performance requirements and satisfy the constraints of the system.
A reference trajectory for the subsystems of a redundant positioning system must ensure that numerous constraints are satisfied. These constraints include, but are not limited to, the physical limitations of the positioning subsystems (such as a stroke constraint, which is the allowed range of motion of an actuator), and operational constraints, such as maximal operational velocities and accelerations of the machine and of each positioning subsystem.
Some prior art systems use a combination of limiter and dead-band elements to compute reference trajectories that do not violate stroke constraints. For example, U.S. Pat. No. 5,262,707 describes cooperative position control of a redundant system including a fine and a coarse movement mechanism. A general purpose positioning control method is used to control the coarse movement mechanism such that the fine subsystem movement does not exceed a range of motion of the subsystem. This is achieved by adjusting gains of the coarse movement subsystem. This is an ad hoc method that does not provide any guarantee that the constraints are satisfied for all the possible operating conditions of the machine.
U.S. Pat. Nos. 5,452,275 and 7,710,060 describe two-stage fast and slow actuator control systems. Frequency separation and filtering approaches in frequency and amplitude were adopted to compute trajectory for the fast and slow subsystems, but no constraints are considered.
U.S. Pat. No. 5,801,939 considers the issue of range saturations in a redundant positioning system with a coarse and a fine positioner. The fine positioner has a faster dynamics but is limited by its small stroke range. To address this problem, a model of the fine positioning subsystem along with a limiter is used in the control loop of the coarse subsystem.
U.S. Pat. Nos. 5,751,585 and 6,706,999 describe a triply redundant laser beam positioner system that uses a combination of fast steering mirrors and galvanometer driven mirrors along with an X-Y table. Low and mid pass filters are used to perform frequency separation. The low frequency component of trajectory is followed by the X-Y table, the low frequency positioning error is sent to a mid pass filter, the output of which is tracked by the galvano mirrors. The remainder high frequency components are then sent to a controller for a fast steering mirror. To mitigate the effect of phase shift introduced by the filters, two delay elements are utilized. The introduction of the delay elements increases the system throughput by decreasing the travel time between points. Again, the constraints of the system are not considered.
In U.S. Application Publication 20130190898, model predictive control is used to compute trajectories for different stages of the machine while explicitly enforcing physical and operational constraints. The proposed approach uses a terminal state constraint and relies on the availability of a feasible trajectory. However, in the absence of such feasible trajectory the control system may fail to compute a trajectory that satisfies all of the constraints.
None of the conventional methods for the control of redundant positioning systems have managed to address the problem of computing reference trajectories that guarantee constraint satisfaction. Manual tuning controller gains or filter crossover frequencies has been used to address the constraint problem without rigorous guarantees. But this is undesirable because the system performance, e.g., throughput, is dependent on these gains and filter frequencies. To avoid constraints, the performance of the machine is reduced. Furthermore, regardless of the gain magnitudes and the filter frequencies, constraint satisfaction is not guaranteed for all the different desired motion of the machine. In addition, tuning the filter gains, the delay elements, the limiters, and the dead-band elements is a task for which no systematic procedure is available, and hence can be time consuming, error prone, and may result in the reduced machine performance, in terms of throughput and precision.